Let the father's mass be M sos that the son's mass must be 2M/5. Let the father's initial speed be V, and the son's v.
(1/2)MV^2 = (1/3)(2M/5)v^2
which leads to
V^2 = (4/15)v^2

(1/2)M(V +1.5)^2 = (2M/5) v^2
V^2 + 3V + 2.25 = (4/5) v^2

3V^2 = (4/5)v^2
Now you can eliminate v.

2V^2 -3V -2.25 = 0
That can be solved for a positive V using the quadratic equation. Chack my math.

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